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Finding coordinates given 3-dimensional vectors

  • Thread starter mystmyst
  • Start date
  • #1
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Homework Statement



[tex]
\begin{align*}
\vec{u} = 2 \hat{x} - 3 \hat{y} + \hat{z}
\vec{v} = \hat{x} - \hat{y} - \hat{z}
\end{align*}
[/tex]

Given a parallelogram that's vertex is at the origin (0,0,0) and is created by two vectors u and v:

a) find where the fourth vertex is of the parallelogram
b) find the length of the two diagonals


The Attempt at a Solution



a) since it's a parallelogram, the fourth point is at u + v = [tex]3 \hat{x} - 4 \hat{y} [/tex] ------- I'm not sure if the answer is supposed to be in this form or in form (3,-4,0)

b) I'm not sure about this one. By length, do they mean distance? Should I use the distance formula between two points? Or do they possibly mean vector addition/subtraction?

Thanks!
 
Last edited:

Answers and Replies

  • #2
75
0
Hi mysmyst.

a) The vector u+v points to the fourth vertex, whose coordinates are (3,-4,0)

b) You may calculate the vectors that follow the diagonals, from u and v, and then calculate their modules.
 
  • #3
57
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the big diagonal is obviously u+v. but is the little diagonal u-v or v-u? and how do I tell which it is in general?

Thanks!
 
  • #4
75
0
The little diagonal is (v-u) and also (u-v). It doesn't matter. It depends on which sense you see it.
 
  • #5
57
0
o. that was silly (:

Thanks!

is there a thanks button?
 

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